Hmm. I just feel like, either we hear about those object in the story, in which case they're not "seemingly insignificant", or we don't hear about them... in which case we can't judge their significance because we don't know about them.
I suppose a character could have an object which is mentioned, but its significance isn't mentioned. Like, "She wore a necklace in the shape of a crescent moon. Anyway, moving on...". But then we're in "secret author knowledge" territory, no?